Reassessing the importance of the colour-singlet contributions to direct $J/ + W$ production at the LHC and the Tevatron

We show that the colour-singlet contributions to the hadroproduction of $J/\Psi$ in association with a W boson are sizable, if not dominant over the colour-octet contributions. They are of two kinds, $sg\toJ/\Psi+c+W$ at $\alpha^3s\alpja$ and $q\overline q' \to\gamma^\star /Z ^\star W\to J/\Psi W$ at order $\alpha^3$. These have not been considered in the literature until now. Our conclusion is that the hadroproduction of a $J/\Psi$ in association with a W boson cannot be claimed as a clean probe of the colour-octet mechanism. The rate are small even at the LHC and it will be very delicate to disentangle the colour-octet contributions from the sizable colour-singlet ones and from the possibly large double-parton-scattering contributions. During this analysis, we have also noted that, for reactions such as the production of a $J/\Psi$ by light quark–antiquark fusion, the colour-singlet contribution via an off-shell photon is of the order of the expectation from the colour-octet contribution via an off-shell gluon. This is relevant for inclusive production at low energies close to the threshold. Such an observation also likely extends to other processes naturally involving light-quark annihilation.